STNB2026 (39th edition)
Explicit base-change lifts of modular forms
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Resumen
In this talk, we introduce explicit formulas for two known Langlands base-change results: Doi—Naganuma lifting in the case of real quadratic number fields and its generalisation to totally real cyclic number fields of prime degree by Saito. Moreover, we talk about the on-going work of generalising Saito’s results to the compositum of two totally real cyclic extensions of prime degrees. We call the results above explicit since they provide the Fourier coefficients for the base-change lifted Hilbert modular forms, which we know exist thanks to Arthur and Clozel in the cyclic case, or more in general, thanks to Dieulefait.
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